Right triangle calculator (a,c)

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R


You have entered cathetus a and hypotenuse c.

Right scalene triangle.

Sides: a = 200   b = 3273.897676074   c = 3280

Area: T = 327389.6766074
Perimeter: p = 6753.897676074
Semiperimeter: s = 3376.948838037

Angle ∠ A = α = 3.49658136324° = 3°29'45″ = 0.06110134579 rad
Angle ∠ B = β = 86.50441863676° = 86°30'15″ = 1.51097828689 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 3273.897676074
Height: hb = 200
Height: hc = 199.6287851265

Median: ma = 3275.424363672
Median: mb = 1649.121097798
Median: mc = 1640

Inradius: r = 96.94883803712
Circumradius: R = 1640

Vertex coordinates: A[3280; 0] B[0; 0] C[12.19551219512; 199.6287851265]
Centroid: CG[1097.398837398; 66.54326170883]
Coordinates of the circumscribed circle: U[1640; -0]
Coordinates of the inscribed circle: I[103.0521619629; 96.94883803712]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.5044186368° = 176°30'15″ = 0.06110134579 rad
∠ B' = β' = 93.49658136324° = 93°29'45″ = 1.51097828689 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a hypotenuse c

a = 200 ; ; c = 3280 ; ;

2. From cathetus a and hypotenuse c we calculate cathetus b - Pythagorean theorem:

c**2 = a**2+b**2 ; ; b = sqrt{ c**2 - a**2 } = sqrt{ 3280**2 - 200**2 } = 3273.897 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 200 ; ; b = 3273.9 ; ; c = 3280 ; ;

3. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 200+3273.9+3280 = 6753.9 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6753.9 }{ 2 } = 3376.95 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3376.95 * (3376.95-200)(3376.95-3273.9)(3376.95-3280) } ; ; T = sqrt{ 107184000000 } = 327389.68 ; ;

6. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 327389.68 }{ 200 } = 3273.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 327389.68 }{ 3273.9 } = 200 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 327389.68 }{ 3280 } = 199.63 ; ;

7. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 200**2-3273.9**2-3280**2 }{ 2 * 3273.9 * 3280 } ) = 3° 29'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3273.9**2-200**2-3280**2 }{ 2 * 200 * 3280 } ) = 86° 30'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3280**2-200**2-3273.9**2 }{ 2 * 3273.9 * 200 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 327389.68 }{ 3376.95 } = 96.95 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 200 }{ 2 * sin 3° 29'45" } = 1640 ; ;
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